Masonic Mathematics: The 47th Problem of Euclid

Past Master's Jewel, 1823. Thomas Harper (ca. 1735-1832). London. 2017.018.2. Photograph by David Bohl.

Do you remember the Pythagorean Theorem? This geometric figure, also known as the 47^th Problem of Euclid, represents the idea that the area of the two smaller squares created by using the lines of a right-angle triangle as bases is equal to the area of the largest square created in the same way. It is stated mathematically as c² = a² + b² in which “c” is the hypotenuse (longest side) and “a” and “b” are the other two sides. Like many geometric expressions, it’s difficult to describe with words, but its meaning is fairly comprehensible visually.

Luckily, then, this symbol appears on Masonic aprons, jewels, pitchers, quilts, lantern slides, mark medals, tracing boards, and other decorative and ritual material in the collection of the Scottish Rite Masonic Museum & Library. Freemasonry draws symbols from a variety of sources, including geometry, to teach instructive lessons to its members.

This geometric figure has two names associated with some of mathematics’ historic giants: Pythagoras (ca. 570 B.C.E. – ca. 495 B.C.E.) and Euclid (ca. 300 B.C.E.). However, its roots reach back further. Babylonians (ca. 1900 - 1600 B.C.E) used it to solve geometric problems that involved right triangles. In Freemasonry, it is often called the 47^th Problem of Euclid. This symbol is introduced in the 3^rd or Master Mason degree.

The object shown here, an engraved Past Master’s jewel, bears a particularly compelling visual representation of this noteworthy geometric figure. English silversmith Thomas Harper (ca. 1735-1832) crafted this jewel, marking it with his initials and British silver hallmarks. The “leopard’s head” mark indicates that the silver was hallmarked in London after 1822. The lowercase “h” indicates Harper made the item in 1823, according to the “date letters” that were used in British silver.

Past Master's Jewel, 1823. Thomas Harper (ca. 1735-1832). London. 2017.018.2. Photograph by David Bohl.

This form of a Past Master’s jewel featuring a right-angle square with a rectangle engraved with a depiction of the 47^th Problem of Euclid, was popular in English lodges in the early decades of the 1800s. This style of jewel inspired Past Master’s jewels in Pennsylvania, which often have a right-angle square bearing a suspended rectangle with the geometric figure engraved on it.

This fascinating Past Master’s jewel is currently on view at the museum in "What's in a Portrait?" and in our online exhibition. You can see other items in the museum’s collection that bear the 47^th Problem of Euclid on our searchable online collections database.

Museum Staff Attend ICHF Conference in Edinburgh, Scotland

Scottish Rite Masonic Museum & Library staff members Aimee Newell, Hilary Anderson Stelling, and Catherine Swanson attended the ICHF conference in Edinburgh, Scotland from May 24 through May 26, 2013.  This was an extraordinary opportunity to hear the latest scholarship on the history of Freemasonry.  The location was  ideal--being held in Edinburgh, Scotland this year. 

Papers were delivered at the Grand Lodge of Scotland (as seen above).  Aimee Newell, Director of Collections, and Hilary Anderson Stelling, Director of Exhibitions, gave papers.  All three attended lecture sessions and networked with colleagues from around the world. 

Newell and Stelling presented their papers on the first day of the conference as part of a session focusing on American Freemasonry. 

Newell's paper was entitled, "A Ludicrous Affair:  Harmonic Lodge and Boston Freemasonry in the 1790s."  Using Harmonic Lodge as a case study, Newell explored how the internal dissent in Boston Freemasonry during the 1790s.  In 1797, the Grand Lodge of Massachusetts voted to revoke the charter of Harmonic Lodge because of improper behavior, with Grand Master Paul Revere (1734-1818) voting "Yes" and Isaiah Thomas voting "No."  During the 1790s the Grand Lodge of Massachusetts was trying to establish its authority and this act can be seen as an attempt to maintain a sense of order within the fraternity. Newell gave convincing evidence of this during her presentation. For two years after the incident with Harmonic Lodge, starting in 1798, no new lodges were chartered in Massachusetts. 

Stelling's paper was entitled, "Elucidating the Various Masonic Emblems:  The Influence of Jeremy Cross and Amos Doolittle's Engravings on Nineteenth Century American Masonic Material and Visual Culture."  She examined the creative collaboration between Jeremy Cross (1783-1860) and Amos Doolittle (1754-1832) in making The True Masonic Chart or Hieroglyphic Monitor and the influence their work had on shaping visual expression in America.  Through extensive analysis of objects, Cross's diary, correspondence, and Masonic publications from the 1800s, Stelling gave a compelling argument for Cross and Doolittle's long-term impact.

The highlights of the conference for Swanson were attending keynote addresses on "The Rise and Fall of Empires: Britain's and the UGLE's Compared" by J. W. Daniel (United Kingdom) and "The Rituals of the Union" by Jan Snoek (Netherlands).  Among the sessions she attended were "The Royal Arch and the 1813 English Union," "Freemasonry in Scotland," and "Enlightenment Visions of Masonry" which were all illuminating.  She enjoyed meeting scholars including Diane Clements, Director, Susan Snell, Archivist, and Martin Cherry, Librarian, from the Library and Museum of the United Grand Lodge of England.